(5a-3)(6a+5)=2

Solution for (5a-3)(6a+5)=2 equation:

(5a-3)(6a+5)=2

We move all terms to the left:

(5a-3)(6a+5)-(2)=0

We multiply parentheses ..

(+30a^2+25a-18a-15)-2=0

We get rid of parentheses

30a^2+25a-18a-15-2=0

We add all the numbers together, and all the variables

30a^2+7a-17=0

a = 30; b = 7; c = -17;
Δ = b2-4ac
Δ = 72-4·30·(-17)
Δ = 2089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{2089}}{2*30}=\frac{-7-\sqrt{2089}}{60}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{2089}}{2*30}=\frac{-7+\sqrt{2089}}{60}
$